Advanced Transmission Techniques in WiMAX Part 6 pdf

This is strictly related to the diversity order that G2 achieves equal to g d =N×M=4, whereas the SM and the Golden code with a linear receiver get a diversity order of 1 Forward erro

OFDMA Air Interface and System Level configuration

Subcarrier Permutation Distributed (PUSC) and Contiguous (Band AMC)

Channel coding1 Turbo coding with rates: 1/3, 1/2, 2/3, ¾

Channel estimation (CQI) Ideal without any delay

Number of transmit antennas, M {1,2,4}

Number of receive antennas, N {1,2,4}

Rate (spectral efficiency) {2,4,8} bits per channel use (bpcu)

Table 1 TACS evaluation framework system parameters

where for each realization a tile or a subchannel (specified in each analysis) is transmitted

In case of Partial Usage Subcarrier permutation (PUSC), the tile is formed by 4 subcarriers and 3 symbols, where 4 tones are dedicated to pilots as defined in IEEE 802.16e [17] For the Band Adaptive Modulation and Coding (AMC) permutation scheme, each bin (equivalent to the tile concept) is comprised by 9 subcarriers where 1 tone is used as pilot Perfect channel

estimation is assumed at the receiver Every log 2(Z) bits are mapped to one symbol The channel models used are uncorrelated Rayleigh (H~CN(0,1)) and the ITU Pedestrian A [38]

In both cases the channel is considered constant within a tile (block fading channel model) In

case of uncorrelated Rayleigh the channel between tiles is uncorrelated, whereas in the ITU PedA case the channel is correlated both in frequency and time

4.4.3 MIMO reference and simulation results

In Fig 6, the reference performance for a fixed rated is depicted for N=2 when no transmit

antenna selection neither code selection are used For uncorrelated Rayleigh channel, we can

observe that for low data rate, i.e R={2,4}, the Alamouti code outperforms the rest of the schemes This is strictly related to the diversity order that G2 achieves equal to g d =N×M=4,

whereas the SM and the Golden code with a linear receiver get a diversity order of

1 Forward error correction is consider only for the throughput maximization case, where the LUT used

to predict the BLER as a function of the ESINR, are obtained using the Duo-Binary Turbo code defined for IEEE 802.16e

g d =(N – M + 1)=1 At higher data rates (R>8), all the codes perform similarly in the analysed

SNR range despite of the different diversity order between them

4.4.4 TACS performance under bit error rate minimization criterion

In Fig 7 and Fig 8, the bit error rate performance using TACS is shown having a fixed rate

R=4 Fig 7 shows the improvement due to the increase in M a and also the performance

achieved when combined with code selection It can be observed how the TAS increases the

diversity order, leading to a large performance increase for the SM and Golden subsets It is

very important to notice that despite the diversity increase for all the LDC subsets, SD and

SIMO schemes still perform better when each code is evaluated independently However, in

Fig 8, we can observe that when the code selection is switched on, SIMO and Golden

subsets are selected most times, while the usage of SIMO increases with the SNR and the

usage of SM and the Golden code increases with M a Furthermore, the achieved

improvement by the TACS is clearly appreciated in Fig 7, where an SNR improvement of

approximately 1dB is obtained for M a={3,4} It is also surprising that the SM code is rarely

selected knowing that the Golden code should always outperform SM since it obtains a

higher diversity However, as it is observed in Fig 8, for less than 5% of the channel

realizations the SM may outperform slightly the Golden code Whether the singular value

decomposition of the effective channel H is analysed when SM is selected, it has been

observed that when all singular values are very close, both the SM and the Golden code lead

to very similar performances, therefore no matter which one is selected

In Fig 9 and Fig 10, the performance using the TACS is again analysed for R=8 In Fig 9 the

different diversity orders of SD, SM, and the Golden Code are illustrated We can appreciate

here that the SM and the Golden code show the best performance when M a={3,4}, and also

for M a=2 when SNR≤18dB Furthermore the increase in the diversity order due to TACS can

be observed in both Fig 7 and Fig 9 The maximum diversity order (g d = M a N) is achieved

since at least one LDC (SIMO and G2) from those in the codebook are able to achieve the

maximum diversity order

Moreover, the BER using the TACS is equivalent to that obtained from the SISO scheme

(referred as SISOeq in the plots) over a Rayleigh fading channel with the same rate R, a

diversity order g d =M a N and a coding gain equal to  The performance of this equivalent

SISO scheme, in terms of the bit error rate probability P b, can be obtained directly by close

expressions that are found in [41][42] and applying the Craig’s formula in [43],

b b

where b = · / log2(Z), x means the smallest integer of x, and Z is the modulation order

of the Z-QAM modulation

The values of  for different combinations of M a ={2,3,4}, N={2,3,4} and R={4,8} are depicted

in Table 2 These values have been obtained adjusting the BER approximation in Eq (28) to the empirical BER As shown in Fig 7 and Fig 9 the performance of the TACS schemes is perfectly parameterized under the equivalent SISO model Notice also that the power gain is

constant across the whole SNR range

Table 2 Coding gain  for the TACS proposal with M a ={2,3,4}, N={2,3,4}, and R={4,8}

Fig 6 Uncoded BER for uncorrelated Rayleigh channel with MMSE detector and N=2

Fig 7 Uncoded BER performance when N=2, R=4, M a={2,3,4} for uncorrelated MIMO Rayleigh channel and MMSE linear receiver

Fig 8 LDC selection statistics with N=2, R=4, M a={2,3,4} for uncorrelated MIMO Rayleigh channel and MMSE linear receiver

Fig 9 Uncoded BER performance when N=2, R=8, M a={2,3,4} for uncorrelated MIMO Rayleigh channel and MMSE linear receiver

Fig 10 LDC selection statistics when N=2, R=8, M a={2,3,4} for uncorrelated MIMO Rayleigh channel and MMSE linear receiver

4.4.5 TACS performance under throughput maximization criterion

In this section the performance of the TACS adaptation scheme in case the throughput is maximized (see Eq.(27)) is analysed Then, for such adaptation scheme, the antenna set and the LDC code that maximizes the throughput is selected In addition, the highest MCS (in the sense of spectral efficiency) that achieves a BLER<0.01 (1%) is also selected The look-up-table used for mapping the ESINR to the BLER is shown and described in [14] In the scenarios considered, the minimum allocable block length according the IEEE 802.16e

standard was selected [17] (i.e the number of sub-channels N sch occupied per block varies

between 1 and 4) The number of available antennas is M a =2 whereas N=2

In Fig 11 and Fig 12, the spectral efficiency achieved by TACS with adaptive Modulation and Coding (AMC) as well as the LDC statistics are shown For Spatial Multiplexing (SM),

two encoding options named Vertical Encoding (VE) and Horizontal Encoding (HE) are

considered For the first scheme, VE, the symbols within the codeword apply the same MCS format, whereas for the second, HE, each symbol may apply a different MCS Clearly the

first is more restrictive since is limited by the worst stream (min(ESNR q)) whereas the second

is able to exploit inter-stream diversity at the expense of higher signalling requirements (at

least twice as that required with VE in case of M=2)

Depicted performances shown that at low SNRs (SNR<13dB), the SIMO and Alamouti achieve the highest spectral efficiencies (something that has been already obtained in several previous works [10]) However, as the SNR is increased, the codes with higher multiplexing capacity (e.g the SM and the Golden code) are preferred It could be also observed that the

SM with VE implies a loss of around 2dB compared to the Golden code, but when HE is used, the Golden code is around 0.5dB worse than the SM-HE

Fig 11 Spectral efficiency under TACS with throughput maximization criterion with M a=2,

N=2, adaptive MCS and MMSE receiver for an uncorrelated MIMO Rayleigh channel

Fig 12 LDC selection statistics under TACS with throughput maximization criterion with

M a =2, N=2, adaptive MCS and MMSE receiver for an uncorrelated MIMO Rayleigh channel

To gain further insights of the TACS behaviour, the statistics of LDC selection as a function

of the average SNR are plotted in Fig 12 We can clearly appreciate that at low SNR the preferred scheme is SIMO where all the power is concentrated in the best antenna, while as

the SNR is increased full rate codes (Q=M) are more selected since they permit to use lower

size constellations Moreover, comparing SM-VE with SM-HE, we can observe that SM-HE

is able to exploit the stream’s diversity and hence achieves a higher spectral efficiency than

if the Golden code is used Actually, at average SNR=12, the SM with HE is the scheme selected for most frames, even more than SIMO These results show that in case of linear receivers (e.g MMSE) the TACS scheme with AMC gives a noticeable SNR gain (up to 3dB)

in a large SNR margin (SNR from 6 to 18dB) and also is a good technique to achieve a smooth transition between diversity and multiplexing

5 MIMO in IEEE 802.16e/m

The use of MIMO may improve the performance of the system both in terms of link reliability and throughput As it was discussed in previous sections, both concepts pull in

different directions, and in most cases a trade-off between both is meet by each specific

space-time code From a system point of view, and due to the inherent time/freq variability

of the wireless channel, no code is optimal for all channel conditions, and at most, the codes

can be optimized according to the ergodic properties of the channel In fact, this is the

reason why the TACS scheme is able to bring significant gain compared to a scheme where

the same space-time code is always used This situation is well-known and it is the reason

why in most of the Broadband Wireless Access (BWA) systems, the number of space-time

codes is increasing

In IEEE 802.16e/m, two types of MIMO are defined, Single User MIMO and Multiuser

MIMO, the first corresponding to the case where one resource unit (the minimum block of

frequency-time allocable subcarriers) is assigned to a single user, and the second when this

one is shared among multiple users

In case of two transmit antennas, IEEE 802.16e/m defines two possible encoding schemes

referred as Matrix A and Matrix B Matrix A corresponds to the Alamouti scheme, while

Matrix B corresponds to the Spatial Multiplexing (SM) case In case of using SM, WiMAX

allows both Vertical Encoding (VE) and Horizontal Encoding (HE) In the first case, VE, all

the symbols are encoded together and belong to the same layer In addition to Matrix A and

Matrix B, IEEE 802.16 also defines a Matrix C which corresponds to the Golden Code This

code is characterized for providing the highest spatial diversity for the spatial rate R=2 In

case of 3 and 4 transmit antennas, WiMAX also defines the encoding schemes of Matrix A,

Matrix B, and Matrix C, all of them providing different trade-offs between diversity and

spatial multiplexing

The list of combinations is even longer since WiMAX allows antenna selection and antenna

grouping, therefore, the list of encoding matrices also includes the possibility that not all

antennas are used, and only a subset are selected (the list of matrices in Table 3 do not show

this possibility) In case not all the antennas are used, the power is normalized so that the

same power is transmitted disregard of the number of active antennas

Besides the possibility to select among any of the previous coding matrices, IEEE 802.16e/m

also allows the use of precoding In this case, the space-time coding output is weighted by a

matrix before mapping onto transmitter antennas

where x is M t×1 vector obtained after ST encoding, where Mt is the number of streams at the

output of the space time coding scheme The matrix W is a M×M t weighting matrix where M

is the number of transmit antennas The weighting matrix accepts two types of adaptation

depending on the rate of update, named short term closed-loop precoding and long term

closed-loop precoding

In the later IEEE 802.16m, the degrees of flexibility has been broadened, allowing several

kinds of adaptation [44] On top of this, IEEE 802.16m includes also ST codes for up to 8

transmitter antennas, enabling the transmission at spectral efficiencies as high as

30bits/sec/Hz which become necessary to achieve the very high throughputs demanded for

IMT-Advanced systems [45]

M Nmin T Q R MIMO Encoding Matrix Name

s0 s1

Spatial Multiplexing (a.k.a Matrix B)

Golden Code (a.k.a Matrix C)

43

6 Summary

The use of multiple antenna techniques at transmitter and receiver sides is still considered a hot research topic where the channel capacity can be increased if multiple streams are multiplexed in the spatial domain The study on the trade-off between diversity and multiplexing has motivated the emergence of many different space-time coding architectures where most of the proposed schemes lie in the form of Linear Dispersion Codes Furthermore, as it was shown by the authors in previous sections, when the transmitter disposes of partial channel state information, robustness and throughput can be very significantly improved One of the simplest adaptation techniques is the use of antenna selection, which increases the diversity of the system up to the maximum available (g d=M a N a) On the other hand, when transmit antenna selection is combined with code selection a coding gain is achieved In this chapter, a joint Transmit Antenna and space-time Coding Selection (TACS) scheme previously proposed by the authors has been described The TACS algorithm allows two kind of optimization: i) bit error rate minimization, and ii)

throughput maximization One important result obtained from these studies is that the number of required space-time coding schemes is quite low In fact, previous studies by the author have shown that in case of spectral efficiencies of 8bits/second/Hertz or lower, using SIMO, Alamouti, SM, and the Golden code is enough to maximize the performance (for higher rates, codes with higher spatial rate would be required) Furthermore, the worse performance achieved by linear receivers (e.g ZF, MMSE) is compensated by the TACS scheme, which allows to achieve performances close to those obtained with the non-linear receivers (e.g the Maximum Likelihood) with much lower computational requirements As

a final conclusion, it can be considered that transmit antenna selection with linear dispersion code selection can be an efficient spatial adaptation technique whose low feedback requirements make it feasible for most of the Broadband Wireless Access systems, especially

in case of low mobility

7 Acronyms

3GPP 3rd Generation Partnership Project

AWGN Additive White Gaussian Noise

BLER Block Error Rate

CSI Channel State Information

FDD Frequency Division Duplexing

LDC Linear Dispersion Codes

LTE Long Term Evolution

MCS Modulation and Coding Scheme

MIMO Multiple Input Multiple Output

MMSE Minimum Mean Square Error

OSTBC Orthogonal Space-Time Block Code

QAM Quadrature Amplitude Modulation

SIMO Single Input Multiple Output

SISO Single Input Single Output

SM Spatial Multiplexing

SNR Signal To Noise Ratio

STBC Space-Time Block Code

TACS Transmit Antenna and (space-time) Code Selection

TDD Time Division Duplexing

UPA Uniform Power Allocation

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